"Barn Burning" is a wonderful short story. It's a heartbreaking story, but that doesn't change its quality. Faulkner likely didn't have a singular purpose in writing this story, so your best option to analyze probable purposes is to examine themes that the story puts before readers. One such theme is that loyalty to family and loyalty to moral standards are not always the same thing and can cause great conflict.
Readers see this theme and conflict in the characters of Abner Snopes and Sarty. Abner is Sarty's father, and Abner is a hard and bitter man. He's callous to his own family members, and he's even more gruff with people he believes shouldn't have power over him. As Abner's son, Sarty feels that he has to love and support his father, and Abner insists that protecting your "blood" is one of life's basic rules.
You got to learn to stick to your own blood or you ain’t going to have any blood to stick to you.
Despite this kind of parental influence, Sarty manages to have a strong moral compass and a strong sense of justice. This is why he knows that burning barns and lying about it is wrong. Abner believes no such thing, and he thinks that Sarty should blindly follow his father's lead and protect his family regardless of personal feelings about morals and justice. As the story continues, readers see the conflict between Abner and Sarty grow. We also see Sarty's internal conflict grow, and he is forced to make the decision between doing what it right and protecting his father. If nothing else, Faulkner shows readers that the choice is not an easy choice.